| step type | requirements | statement |
0 | deduction | 1 | ⊢ |
1 | instantiation | 2, 3, 4, 13, 5, 6 | , ⊢ |
| : , : , : |
2 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.singular_constructive_dilemma |
3 | instantiation | 7, 9 | ⊢ |
| : , : |
4 | instantiation | 8, 9 | ⊢ |
| : , : |
5 | deduction | 10 | , ⊢ |
6 | deduction | 11 | , ⊢ |
7 | axiom | | ⊢ |
| proveit.logic.booleans.disjunction.left_in_bool |
8 | axiom | | ⊢ |
| proveit.logic.booleans.disjunction.right_in_bool |
9 | instantiation | 12, 13 | ⊢ |
| : |
10 | instantiation | 38, 14, 116 | , , ⊢ |
| : , : |
11 | instantiation | 38, 15, 116 | , , ⊢ |
| : , : |
12 | theorem | | ⊢ |
| proveit.logic.booleans.in_bool_if_true |
13 | instantiation | 16, 164, 17 | ⊢ |
| : , : |
14 | instantiation | 19, 20, 21, 18 | , , ⊢ |
| : , : , : |
15 | instantiation | 19, 20, 21, 22 | , , ⊢ |
| : , : , : |
16 | theorem | | ⊢ |
| proveit.numbers.ordering.less_or_greater_eq |
17 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
18 | instantiation | 44, 23, 24 | , , ⊢ |
| : , : |
19 | theorem | | ⊢ |
| proveit.logic.sets.unification.membership_folding |
20 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
21 | instantiation | 152 | ⊢ |
| : , : |
22 | instantiation | 48, 25, 26 | , , ⊢ |
| : , : |
23 | instantiation | 31, 181, 36, 174, 27 | , , ⊢ |
| : , : , : |
24 | instantiation | 29, 28 | , , ⊢ |
| : , : |
25 | instantiation | 29, 30 | , , ⊢ |
| : , : |
26 | instantiation | 31, 47, 190, 174, 32 | , , ⊢ |
| : , : , : |
27 | instantiation | 38, 66, 33 | , , ⊢ |
| : , : |
28 | instantiation | 35, 47, 190, 174, 34 | , , ⊢ |
| : , : , : |
29 | theorem | | ⊢ |
| proveit.logic.sets.membership.unfold_not_in_set |
30 | instantiation | 35, 181, 36, 174, 37 | , , ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.in_interval |
32 | instantiation | 38, 39, 63 | , , ⊢ |
| : , : |
33 | instantiation | 51, 151, 169, 40, 41, 42*, 43* | , , ⊢ |
| : , : , : |
34 | instantiation | 44, 45, 46 | , , ⊢ |
| : , : |
35 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_not_in_interval |
36 | instantiation | 192, 47 | ⊢ |
| : |
37 | instantiation | 48, 49, 50 | , , ⊢ |
| : , : |
38 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
39 | instantiation | 51, 165, 169, 52, 53, 54*, 55* | , , ⊢ |
| : , : , : |
40 | instantiation | 82, 83, 56 | , , ⊢ |
| : , : , : |
41 | instantiation | 69, 56 | , , ⊢ |
| : |
42 | instantiation | 107, 57, 58 | ⊢ |
| : , : , : |
43 | instantiation | 96, 59 | , ⊢ |
| : , : |
44 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.or_if_only_left |
45 | instantiation | 60, 161, 61 | , ⊢ |
| : , : , : |
46 | instantiation | 64, 164, 62, 63 | ⊢ |
| : , : |
47 | instantiation | 188, 175, 187 | ⊢ |
| : , : |
48 | theorem | | ⊢ |
| proveit.logic.booleans.disjunction.or_if_only_right |
49 | instantiation | 64, 65, 164, 66 | ⊢ |
| : , : |
50 | instantiation | 157, 67, 148 | , ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.addition.weak_bound_via_left_term_bound |
52 | instantiation | 162, 164, 68 | , ⊢ |
| : , : |
53 | instantiation | 69, 70 | , , ⊢ |
| : |
54 | instantiation | 71, 156, 154 | ⊢ |
| : , : |
55 | instantiation | 107, 72, 73 | , ⊢ |
| : , : , : |
56 | instantiation | 74, 75 | , , ⊢ |
| : |
57 | instantiation | 135, 191, 198, 140, 137, 141, 156, 143, 144 | ⊢ |
| : , : , : , : , : , : |
58 | instantiation | 76, 156, 143, 77 | ⊢ |
| : , : , : |
59 | instantiation | 122, 78, 79, 80 | , ⊢ |
| : , : , : , : |
60 | axiom | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less |
61 | instantiation | 81, 100 | ⊢ |
| : |
62 | instantiation | 82, 83, 195 | ⊢ |
| : , : , : |
63 | instantiation | 84, 181, 190, 178 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.ordering.not_less_from_less_eq |
65 | instantiation | 196, 172, 85 | ⊢ |
| : , : , : |
66 | instantiation | 167, 181, 190, 178 | ⊢ |
| : , : , : |
67 | instantiation | 86, 87 | ⊢ |
| : |
68 | instantiation | 168, 165 | ⊢ |
| : |
69 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
70 | instantiation | 145, 88, 89 | , , ⊢ |
| : |
71 | theorem | | ⊢ |
| proveit.numbers.addition.commutation |
72 | instantiation | 135, 140, 198, 191, 141, 90, 143, 142, 154 | , ⊢ |
| : , : , : , : , : , : |
73 | instantiation | 91, 154, 143, 92 | , ⊢ |
| : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.negation.nat_pos_closure |
75 | instantiation | 93, 94, 95 | , , ⊢ |
| : |
76 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_13 |
77 | instantiation | 132 | ⊢ |
| : |
78 | instantiation | 133, 154, 156 | ⊢ |
| : , : |
79 | instantiation | 132 | ⊢ |
| : |
80 | instantiation | 96, 97 | , ⊢ |
| : , : |
81 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
82 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
83 | instantiation | 98, 99 | ⊢ |
| : , : |
84 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_upper_bound |
85 | instantiation | 196, 176, 181 | ⊢ |
| : , : , : |
86 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.negative_if_in_neg_int |
87 | instantiation | 126, 100 | ⊢ |
| : |
88 | instantiation | 188, 174, 101 | , ⊢ |
| : , : |
89 | instantiation | 102, 103 | , ⊢ |
| : , : |
90 | instantiation | 152 | ⊢ |
| : , : |
91 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_triple_32 |
92 | instantiation | 132 | ⊢ |
| : |
93 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_is_int_neg |
94 | instantiation | 188, 175, 174 | , ⊢ |
| : , : |
95 | instantiation | 104, 164, 165, 153, 105, 106* | , , ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
97 | instantiation | 107, 108, 109 | , ⊢ |
| : , : , : |
98 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
99 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
100 | instantiation | 110, 127, 111 | ⊢ |
| : , : |
101 | instantiation | 196, 112, 113 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.pos_difference |
103 | instantiation | 115, 116, 114 | , ⊢ |
| : , : , : |
104 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
105 | instantiation | 115, 116, 117 | , ⊢ |
| : , : , : |
106 | instantiation | 118, 143, 119 | ⊢ |
| : , : |
107 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
108 | instantiation | 120, 121 | , ⊢ |
| : , : , : |
109 | instantiation | 122, 123, 124, 125 | , ⊢ |
| : , : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.addition.add_nat_pos_closure_bin |
111 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
112 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.neg_int_within_int |
113 | instantiation | 126, 127 | ⊢ |
| : |
114 | instantiation | 130, 178, 128* | , ⊢ |
| : |
115 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
116 | instantiation | 129, 183 | ⊢ |
| : , : |
117 | instantiation | 130, 178, 131* | , ⊢ |
| : |
118 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_reverse |
119 | instantiation | 132 | ⊢ |
| : |
120 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
121 | instantiation | 133, 154, 143 | , ⊢ |
| : , : |
122 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
123 | instantiation | 135, 140, 198, 191, 141, 136, 142, 138, 134 | , ⊢ |
| : , : , : , : , : , : |
124 | instantiation | 135, 198, 140, 136, 137, 141, 142, 138, 143, 144 | , ⊢ |
| : , : , : , : , : , : |
125 | instantiation | 139, 191, 140, 141, 142, 143, 144 | , ⊢ |
| : , : , : , : , : , : , : , : |
126 | theorem | | ⊢ |
| proveit.numbers.negation.int_neg_closure |
127 | instantiation | 145, 175, 146 | ⊢ |
| : |
128 | instantiation | 147, 148 | ⊢ |
| : |
129 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.right_from_and |
130 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._modabs_in_full_domain_simp |
131 | instantiation | 149, 150 | ⊢ |
| : |
132 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
133 | theorem | | ⊢ |
| proveit.numbers.negation.distribute_neg_through_binary_sum |
134 | instantiation | 196, 166, 151 | ⊢ |
| : , : , : |
135 | theorem | | ⊢ |
| proveit.numbers.addition.disassociation |
136 | instantiation | 152 | ⊢ |
| : , : |
137 | instantiation | 152 | ⊢ |
| : , : |
138 | instantiation | 196, 166, 153 | ⊢ |
| : , : , : |
139 | theorem | | ⊢ |
| proveit.numbers.addition.subtraction.add_cancel_general_rev |
140 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
141 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
142 | instantiation | 155, 154 | ⊢ |
| : |
143 | instantiation | 196, 166, 164 | ⊢ |
| : , : , : |
144 | instantiation | 155, 156 | ⊢ |
| : |
145 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.pos_int_is_natural_pos |
146 | instantiation | 157, 158, 159 | ⊢ |
| : , : , : |
147 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_non_neg_elim |
148 | assumption | | ⊢ |
149 | theorem | | ⊢ |
| proveit.numbers.absolute_value.abs_neg_elim |
150 | instantiation | 160, 161 | ⊢ |
| : , : |
151 | instantiation | 162, 164, 163 | ⊢ |
| : , : |
152 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
153 | instantiation | 168, 164 | ⊢ |
| : |
154 | instantiation | 196, 166, 165 | ⊢ |
| : , : , : |
155 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
156 | instantiation | 196, 166, 169 | ⊢ |
| : , : , : |
157 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_less_eq |
158 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.less_0_1 |
159 | instantiation | 167, 187, 185, 180 | ⊢ |
| : , : , : |
160 | theorem | | ⊢ |
| proveit.numbers.ordering.relax_less |
161 | assumption | | ⊢ |
162 | theorem | | ⊢ |
| proveit.numbers.addition.add_real_closure_bin |
163 | instantiation | 168, 169 | ⊢ |
| : |
164 | instantiation | 196, 172, 170 | ⊢ |
| : , : , : |
165 | instantiation | 196, 172, 171 | ⊢ |
| : , : , : |
166 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
167 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.interval_lower_bound |
168 | theorem | | ⊢ |
| proveit.numbers.negation.real_closure |
169 | instantiation | 196, 172, 173 | ⊢ |
| : , : , : |
170 | instantiation | 196, 176, 174 | ⊢ |
| : , : , : |
171 | instantiation | 196, 176, 175 | ⊢ |
| : , : , : |
172 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
173 | instantiation | 196, 176, 187 | ⊢ |
| : , : , : |
174 | instantiation | 196, 177, 178 | ⊢ |
| : , : , : |
175 | instantiation | 196, 179, 180 | ⊢ |
| : , : , : |
176 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
177 | instantiation | 184, 181, 190 | ⊢ |
| : , : |
178 | instantiation | 182, 183 | ⊢ |
| : , : |
179 | instantiation | 184, 187, 185 | ⊢ |
| : , : |
180 | assumption | | ⊢ |
181 | instantiation | 188, 186, 187 | ⊢ |
| : , : |
182 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.left_from_and |
183 | assumption | | ⊢ |
184 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
185 | instantiation | 188, 190, 189 | ⊢ |
| : , : |
186 | instantiation | 192, 190 | ⊢ |
| : |
187 | instantiation | 196, 197, 191 | ⊢ |
| : , : , : |
188 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
189 | instantiation | 192, 193 | ⊢ |
| : |
190 | instantiation | 196, 194, 195 | ⊢ |
| : , : , : |
191 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
192 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
193 | instantiation | 196, 197, 198 | ⊢ |
| : , : , : |
194 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
195 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos |
196 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
197 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
198 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |